We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century.

Specifically, the methodology of polynomial cointegration is used o test AGW since during the bservation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences whereas greenhouse gases and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance.

On the other hand, we find that greenhouse gas forcing might have had a temporary ffect on global temperature.

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Introduction

Considering the complexity and variety of the processes that ffect Earth’s climate, it is not surprising that a completely satisfactory and accepted account of all the changes that occurred in the last century (e.g. temperature changes in the vast area of the Tropics, the balance of CO2 input into the atmosphere, changes in aerosol concentration and size and changes in solar radiation) has yet to be reached (IPCC, AR4, 2007).

Of particular interest to the present study are those processes involved in the greenhouse effect, whereby some of the longwave radiation emitted by Earth is re-absorbed by some of the molecules that make up the atmosphere, such as (in decreasing order of importance): water vapor, Carbon Dioxide, Methane and nitrous oxide (IPCC, AR4, 25 2007). Even though the most important greenhouse gas is water vapor, the dynamics of its flux in/out of the atmosphere by evaporation, condensation and subsequent precipitation are not understood well enough to be explicitly and exactly quantified.

While much of the scientific research into the causes of global warming has been carried out using calibrated general circulation models (GCMs), since 1997 a new branch of scientific inquiry has developed in which observations of climate change are tested statistically by the method of cointegration (Kaufmann and Stern, 1997, 2002; Stern and Kaufmann, 1999, 2000; Kaufmann et al., 2006a,b; Liu and Rodriguez, 2005; Mills, 2009).

The method of cointegration, developed in the closing decades of the 20th century, is intended to distinguish between genuine and spurious regression phenomena in nonstationary time series (Phillips, 1986; Granger and Engle, 1987). Nonstationary arises when the sample moments of a time series (mean, variance, covariance) depend on time. Spurious regression occurs when unrelated nonstationary time series appear to be significantly correlated because they happen to have time trends.

The method of cointegration has been successful in detecting spurious correlation in economic time series data1. Indeed, cointegration has become the standard econometric tool for testing hypotheses with nonstationary data (Maddala, 2001; Greene, 2012). As noted, climatologists too have used cointegration to analyse nonstationary climate data (Kaufmann and Stern, 1997).

Cointegration theory is based on the simple notion that time series might be highly correlated even though there is no causal 20 relation between them. For the correlation to be genuine, the residuals from a regression between these time series must be stationary, in which case the time series are “cointegrated”.

Since stationary residuals mean-revert to zero, there must be a genuine long-term relationship between the series, which move together over time because they share a common trend. If on the other hand, the residuals are nonstationary, the residuals do not mean-revert to zero, the time series do not share a common trend, and the relationship between them is “spurious” because the time series are not cointegrated.

» How much "Man Made" CO2 Is In The Earth's Atmosphere?
I think ALL of the CO2 in the Earth's Atmosphere is from man.
I'm not sure how much "Man Made" CO2 is in the Earth's Atmosphere.
There is .04% CO2 in the Earth's Atmosphere and of that "Man" has added an extra 4% (1 part in 62,500)